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  • Projectile Motion: Calculating Speed After 3 Seconds - Understanding Vertical Velocity
    You can't determine the speed of the projectile after 3 seconds with only the horizontal component of the initial velocity. Here's why:

    * Vertical Motion: The projectile will be affected by gravity, causing it to accelerate downwards. To calculate its speed, you need the initial vertical velocity component as well.

    * Combined Velocity: The projectile's speed is the magnitude of its total velocity, which is the vector sum of its horizontal and vertical velocities.

    Here's what you need to know to solve the problem:

    * Initial vertical velocity (vy0): This is the upward velocity the projectile is launched with.

    * Acceleration due to gravity (g): Approximately 9.8 m/s².

    To find the speed after 3 seconds:

    1. Calculate vertical velocity (vy) after 3 seconds:

    * vy = vy0 + gt

    2. Find the magnitude of the total velocity:

    * v = √(vx² + vy²)

    Where:

    * vx = 4 m/s (horizontal velocity, constant)

    * vy = vertical velocity after 3 seconds (calculated in step 1)

    Example:

    Let's say the initial vertical velocity (vy0) is 5 m/s.

    1. Vertical velocity after 3 seconds:

    * vy = 5 m/s + (-9.8 m/s²) * 3 s = -24.4 m/s

    * Note: It's negative because the projectile is moving downwards.

    2. Magnitude of total velocity:

    * v = √(4² + (-24.4)²) ≈ 24.7 m/s

    Therefore, to find the speed of the projectile after 3 seconds, you need both the horizontal and vertical components of its initial velocity.

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